Practical Activities on PUFs and TRNGs
2025-10-29
Device Under Test
During this workshop, we will be using the STM32L152RC microcontroller.
256 Kbytes of flash memory
*32 Kbytes of RAM = 262144 bits**
8 Kbytes of data EEPROM
Can be controlled easily through ST-LINK/V2 debugger/programmer
STM32 Discovery
PUF Metrics
Uniformity(d) \(\small = \frac{1}{L} \sum_{l=1}^L R_{d,i}\)
Bit-aliasing(c) \(\small = \frac{1}{D} \sum_{d=1}^D R_{d,c}\)
Reliability \(\small = 1 - \frac{1}{S}\sum_{s=1}^S \tfrac{HD(R_{d,ref}, R_{d,s})}{L}\)
Uniqueness \(\small = \frac{2}{D(D-1)}\sum_{i\neq j} \tfrac{HD(R_i, R_j)}{L}\)
The Hamming Distance between two vectors of equal length is the number of positions at which the corresponding values are different.
Reliability per bit
Measure how reliable each bit is across multiple measurements
\[ Reliability = 1 - \frac{1}{S}\sum_{s=1}^S XOR(R_{i,ref}, R_{l,s}) \]
Where \(S\) is the number of readouts, \(R_{l,ref}\) is the \(l\)-th reference bit and \(R_{l,s}\) is the \(l\)-th bit from readout \(s\).
This level of granularity allows us to select bits valid for PUF or TRNG
You will probably obtain a Reliability per bit distribution similar to this one
Shannon Entropy
Entropy measures the expected amount of information needed to describe the state of the variable. In this context, is the number of bits needed to encode a sequence of bits.
\[H(x) = -\sum_{x\in X} p(x) \log(x)\]
For binary variables \(X\in \{0, 1\}\), where \(p = \mathbb{P}[X=1]\)
\[H(p) = -\left[p\log_2(p) + (1-p)\log_2(1-p)\right]\]
Entropy vs Reliability
Reliability and Entropy share an inverse relationship:
- Responses that are very reliable are usually biased
- Conversely, unbiased responses tend to be unreliable
Study the relationship between Entropy and Reliability
